Exercise · ZW-BINOMIAL-DISTRIBUTION-003 · ★☆☆ Basic

If \(X\) is binomial with \(n=20\) and \(p=0.3\), compute \(\operatorname{Var}(X)\).

Choose one option.

Show answer
  • B. \(4.2\)

Explanation

As a sum of \(n\) independent Bernoulli variables, \(\operatorname{Var}(X)=np(1-p)=20\cdot0.3\cdot0.7=4.2\). The value \(6\) is the mean.

Study Probability and statistics in ZWMath →

Review the concept: Binomial distribution

A binomial variable \(X\) counts the successes \(k\) in \(n\) independent Bernoulli trials with the same success probability \(p\); \(P(X=k)\) is the probability of getting \(k\) successes.

\[P(X=k)=\binom{n}{k}p^{k}(1-p)^{n-k},\quad k=0,1,\dots,n\]

More practice problems: binomial distribution

← ZW-BINOMIAL-DISTRIBUTION-002 ZW-BINOMIAL-DISTRIBUTION-004 →